الفهرس 
Literature ReviewOnly 14 pages are availabe for public view
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Abstract
The primary objective of this thesis is to outline the application of fractional calculus to some electric circuits and projectile motion. Fractional calculus is used to modify existing models that use ordinary derivatives to new models using fractional derivatives. The new models exhibit more realistic results when compared with actual experimental measurements. Fractional calculus is used to model series RLC circuit, parallel RLC circuit and Multiple Feedback Active Low-Pass Filter. A new mathematical model to describe these circuits is introduced. Adomian decomposition method, fractional differential transform method, variational iteration method and Laplace transform method are used to solve these models. The second part of the thesis is concerned with the introduction of a new fractional model that generalizes the equations of projectile motion in nonlinear resistance medium. The fractional differential transform method combined with Adomian polynomials is used to solve this fractional model. The thesis is arranged as follows: In chapter one, a literature review that includes a brief look at the history of fractional calculus and how it was developed. In chapter two, definitions of main types of fractional derivatives and integrals are listed. Fractional order derivative model of a capacitor is introduced. In chapter three, a new fractional model that describes the series RLC circuit, parallel RLC circuit and Fractional order Multiple Feedback Active Low-Pass Filter is introduced. These models are solved by using Laplace transform method, Adomian decomposition method, differential transform method and Variational iteration method. The results are represented graphically for different values of fractional order and the comparison between the numerical results of these methods is introduced. The results obtained in this chapter are published in [149-150]. In chapter four, new fractional model generalizes the projectile motion in nonlinear resistance medium equations. The model is solved by using the fractional differential transform method combined with Adomian polynomials. The results are represented graphically for different values of fractional order. The results in this chapter are submitted for publication. In chapter five, we present concluding remarks about the work achieved in this thesis.